Chapter 11.4, Problem 47E

Solution

To find: The correct option from the given options.

The correct option is (C).

Given information:

Different options are given.

Calculation:

(A): The area under a curve that represents some function $f\left(x\right)$:

It can be computed using Reimann sum or NINT.

(B): The distance travelled when the velocity function is known:

The distance travelled when the velocity function $v\left(t\right)$ is known as ${\displaystyle {\int }_{t_0}^{t_1}v\left(t\right)dt}$ .

(D): The change in a city’s population over a 10-year period, when the rate-of-change function is known:

The change in a city’s population is ${\displaystyle {\int }_0^{10}r\left(t\right)dt}$ , $r\left(t\right)$ is rate function.

(E): The change in a child’s height over a 4-year period, when the rate-of-change function is known.

The change in a child’s height over a 4-year period is ${\displaystyle {\int }_0^{4}r\left(t\right)dt}$ , $r\left(t\right)$ is rate function.

Thus, all the above statements are expressed in terms of numerical integrals except option (C).

If the position function $f\left(x\right)$ is known, then the instantaneous velocity of an object is $\frac{df\left(x\right)}{dx}$ . It’s can’t estimate using a numerical integral.

Thus, the correct option is (C).